Related papers: Compression challenges in large scale PDE solvers
Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central…
PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of…
This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…
In this work we study the problem about learning a partial differential equation (PDE) from its solution data. PDEs of various types are used as examples to illustrate how much the solution data can reveal the PDE operator depending on the…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
With endless amounts of data and very limited bandwidth, fast data compression is one solution for the growing datasharing problem. Compression helps lower transfer times and save memory, but if the compression takes too long, this no…
The life-cycle of a partial differential equation (PDE) solver is often characterized by three development phases: the development of a stable numerical discretization, development of a correct (verified) implementation, and the…
Industry-scale recommender systems face a core challenge: representing entities with high cardinality, such as users or items, using dense embeddings that must be accessible during both training and inference. However, as embedding sizes…
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…
We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…
Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…
Rapidly increasing data sizes in scientific computing are the driving force behind the need for lossy compression. The main drawback of lossy data compression is the introduction of error. This paper explains why many error-bounded…
The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov…
Memory latency, bandwidth, capacity, and energy increasingly limit performance. In this paper, we reconsider proposed system architectures that consist of huge (many-terabyte to petabyte scale) memories shared among large numbers of CPUs.…
Compression algorithms reduce the redundancy in data representation to decrease the storage required for that data. Data compression offers an attractive approach to reducing communication costs by using available bandwidth effectively.…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…